Find the absolute maximum and minimum values of f(x, y) = x³ + y² + 8 on the set D where D is the closed region bounded by y = 0 and y = 36-4x². ▾ Part 1: Critical Points The critical points of fare: Part 2: Boundary Work The boundary of the region can be expressed by 2 curves. Although you need to do calculations over all of the boundary pieces you will only submit your results for one of them. Along y = 36-4x², ƒ can be expressed as a function of one variable g(x) = f(x, Σ )= Σ List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D. ▾ Part 3: Final Results Make sure you do the other computations along the other boundaries before you attempt this section! Σ Find the function's absolute maximums and minimums and where they occur. The absolute maximum of fis: Σ and it occurs at The absolute minimum of fis: and it occurs at Σ Σ Σ
Find the absolute maximum and minimum values of f(x, y) = x³ + y² + 8 on the set D where D is the closed region bounded by y = 0 and y = 36-4x². ▾ Part 1: Critical Points The critical points of fare: Part 2: Boundary Work The boundary of the region can be expressed by 2 curves. Although you need to do calculations over all of the boundary pieces you will only submit your results for one of them. Along y = 36-4x², ƒ can be expressed as a function of one variable g(x) = f(x, Σ )= Σ List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D. ▾ Part 3: Final Results Make sure you do the other computations along the other boundaries before you attempt this section! Σ Find the function's absolute maximums and minimums and where they occur. The absolute maximum of fis: Σ and it occurs at The absolute minimum of fis: and it occurs at Σ Σ Σ
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Find the absolute maximum and minimum values of f(x, y) = x³ + ² + 8 on the set D where D is the closed region bounded by y = 0 and
y = 36-4x².
▾ Part 1: Critical Points
The critical points of fare:
▾ Part 2: Boundary Work
The boundary of the region can be expressed by 2 curves. Although you need to do calculations over all of the boundary pieces you will only
submit your results for one of them.
Along y = 36 - 4x², ƒ can be expressed as a function of one variable
g(x) = f(x,
Σ )=
▾ Part 3: Final Results
List all the points on this side of the boundary which could potentially be the absolute minimum or maximum on D.
Σ
Σ
Make sure you do the other computations along the other boundaries before you attempt this section!
The absolute minimum of f is:
and it occurs at
Find the function's absolute maximums and minimums and where they occur.
The absolute maximum of fis:
Σ
and it occurs at
Σ
Σ
Σ
Σ
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